(X+3)(x+8)=150

Solution for (X+3)(x+8)=150 equation:

(X+3)(X+8)=150

We move all terms to the left:

(X+3)(X+8)-(150)=0

We multiply parentheses ..

(+X^2+8X+3X+24)-150=0

We get rid of parentheses

X^2+8X+3X+24-150=0

We add all the numbers together, and all the variables

X^2+11X-126=0

a = 1; b = 11; c = -126;
Δ = b2-4ac
Δ = 112-4·1·(-126)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-25}{2*1}=\frac{-36}{2}
=-18
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+25}{2*1}=\frac{14}{2}
=7
$